Answer
$0.086$
Work Step by Step
$f_x=y^2 -y \sin (x-1) \\ \implies f_x(1,2)=2^2 -(2) \sin (1-1)=4$
Next, $f_y(x,y) =2xy+\cos (x-1) \\ \implies f_{y}(1,2) =2(1)(2)+\cos (1-1)=5$
$f_{xx}(x,y)=-y \cos (x-1); f_{yy}(x,y)=2x$ and $f_{xy}(x,y) =2y- \sin (x-1)$
The error can be found as:
$|E(x,y)| \leq \dfrac{1}{2} \times (4.3) [ |x-1| +|y-2|)^2$
$\implies E \leq \dfrac{4.3}{2} \times (0.1+0.1)^2 =0.086$
